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Entangled time in flocking: Multi-time-scale interaction reveals emergence of inherent noise

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  • Takayuki Niizato
  • Hisashi Murakami

Abstract

Collective behaviors that seem highly ordered and result in collective alignment, such as schooling by fish and flocking by birds, arise from seamless shuffling (such as super-diffusion) and bustling inside groups (such as Lévy walks). However, such noisy behavior inside groups appears to preclude the collective behavior: intuitively, we expect that noisy behavior would lead to the group being destabilized and broken into small sub groups, and high alignment seems to preclude shuffling of neighbors. Although statistical modeling approaches with extrinsic noise, such as the maximum entropy approach, have provided some reasonable descriptions, they ignore the cognitive perspective of the individuals. In this paper, we try to explain how the group tendency, that is, high alignment, and highly noisy individual behavior can coexist in a single framework. The key aspect of our approach is multi-time-scale interaction emerging from the existence of an interaction radius that reflects short-term and long-term predictions. This multi-time-scale interaction is a natural extension of the attraction and alignment concept in many flocking models. When we apply this method in a two-dimensional model, various flocking behaviors, such as swarming, milling, and schooling, emerge. The approach also explains the appearance of super-diffusion, the Lévy walk in groups, and local equilibria. At the end of this paper, we discuss future developments, including extending our model to three dimensions.

Suggested Citation

  • Takayuki Niizato & Hisashi Murakami, 2018. "Entangled time in flocking: Multi-time-scale interaction reveals emergence of inherent noise," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-21, April.
  • Handle: RePEc:plo:pone00:0195988
    DOI: 10.1371/journal.pone.0195988
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    References listed on IDEAS

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    1. Takayuki Niizato & Yukio-Pegio Gunji, 2012. "Fluctuation-Driven Flocking Movement in Three Dimensions and Scale-Free Correlation," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-1, May.
    2. Yukio-Pegio Gunji & Hisashi Murakami & Takayuki Niizato & Yuta Nishiyama & Takenori Tomaru & Andrew Adamatzky, 2012. "Robust Swarm Model Based on Mutual Anticipation: Swarm as a Mobile Network Analyzed by Rough Set Lattice," International Journal of Artificial Life Research (IJALR), IGI Global, vol. 3(1), pages 45-58, January.
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    Cited by:

    1. Takayuki Niizato & Kotaro Sakamoto & Yoh-ichi Mototake & Hisashi Murakami & Takenori Tomaru & Tomotaro Hoshika & Toshiki Fukushima, 2020. "Finding continuity and discontinuity in fish schools via integrated information theory," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-29, February.

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